All Questions
15
questions
4
votes
1
answer
112
views
How to relate Riemannian and Lorentzian tetrad fields on the same manifold/spacetime?
Consider Gibbons and Hawkings paper wherein a Riemannian metric $\overset{\mathcal{R}}{g}_{\mu\nu}$ and everywhere well defined normalized line field $l_{\mu}$ on spacetime $M$ may be used to ...
- 2,847
0
votes
2
answers
75
views
General Relativistic version of the Lorentz factor
In curved spacetime, the Lorentz factor is different than that in flat spacetime.
Is there any expression that gives the Lorentz factor for any arbitrary metric tensor?
user355398
6
votes
4
answers
1k
views
Twin Paradox (SR): How can we express the comparative length of arbitrary world-lines mathematically?
The simplest and most intuitive way I have found so far for explaining which twin ages less in the Twin Paradox, is that it's the twin who's world-line is the longest (if it's the longest in one ...
- 200
3
votes
3
answers
537
views
Why is proper time $d\tau$ equated to spacetime length $ds$?
Follow-up to this question: Why proper time is a measure of space?.
The selected answer to me tells us why proper time is an invariant quantity, but I'm still wondering why we equate it to $ds$. Can ...
- 1,261
5
votes
1
answer
402
views
Physical Meaning of Pullback metric vs. Effective Spatial Metric
Consider a Riemannian Manifold with a metric tensor $g_{\mu\nu}$ and coordinates $(t, x^i)$. Let us assume that the spacetime is stationary, so $\partial_t g_{\mu\nu} = 0$. At a fixed coordinate time ...
- 709
6
votes
2
answers
403
views
Conflicting definitions of reference frames in general relativity
I'm having trouble understanding what constitutes a reference frame in general relativity as there seem to be several contradictory definitions.
It is my understanding that, in special relativity, ...
- 2,157
14
votes
3
answers
879
views
Why are observers/reference frames able to see themselves moving through time but not through space?
All observers are stationary in their own reference frames.
That is, their space coordinates are constant at all times (in their frame).
However, they can see themselves moving through time.
What ...
- 1,421
0
votes
3
answers
129
views
Is the concept "space" actually needed?
I started making my mind around space and time and recently came to a point where I wondered if the concept of "space" is actually needed to describe physical processes at all and not just some ...
- 41
3
votes
1
answer
58
views
Tracking Spacetime Events
In the linked post: Liouville's Theorem For Spacetime, I indicated the need for tracking the evolution of spacetime events. Is it sufficient to track a spacetime event by placing a particle there ...
- 3,514
0
votes
1
answer
1k
views
What is the metric equation of an accelerating frame of reference? [closed]
Most topics in general relativity speak about the gravity, equivalence principle and the relation of energy mass tensor. How about the simple equation of the metric in 4D space-time of an accelerating ...
- 29
1
vote
1
answer
199
views
Which time is there in the FRW metric?
The FRW metric is given by $$ds^2=dt^2-a^2(t)\Big[\frac{dr^2}{1-kr^2}+r^2(d\theta)^2+(r\sin\theta)^2(d\phi)^2\Big].$$ There is a time $t$ sitting in this metric. In which frame is this time measured?
- 26.8k
0
votes
0
answers
153
views
Frame transformations in curved spacetime
Suppose I have a vector $k^{\alpha}$ in a frame A
A second frame B has a 4-velocity w.r.t frame A of $u^{\mu}$.
How would I determine the original vector in frame B, $k^{\beta}$, for a general (i.e. ...
- 1,751
0
votes
2
answers
492
views
On the derivation of space-time interval
The introduction to GR of Bernard Schutz, writes de space-time interval like this
$\Delta\bar{s}^{2}=M_{\alpha\,\beta}(\Delta x^{\alpha})(\Delta x^{\beta})$
$\Delta\bar{s}^2$ is the space-time ...
3
votes
2
answers
4k
views
How much Gravity is required to stop time?
Clocks free of gravitational influence run faster than those experiencing gravity. Is it possible for gravitational influence to bring time to a stop? Additionally can acceleration affect clocks in ...
- 470
0
votes
2
answers
521
views
Timelike curves in Special Relativity
I have a question that probably might sound silly to most of you.
We know that a natural Lorentz-invariant parametrization of a timelike curve is provided by:
$$\tau$$
the Lorentz-invariant proper ...
- 1,529